Vocabulary
Define the term "variable" in one sentence and give an example using x.
Variable: a symbol that represents an unknown quantity (example: x = number of apples).
Solve: x + 8 = 15
x = 7
Solve: 2x + 5 = 17
x =6
A rectangle has perimeter 30 and length 8. Let w be the width. Write and solve an equation for w.
2(8 + w) = 30 → w = 7
What does "coefficient" mean? Give an example from the expression 7x - 5.
Coefficient: a number multiplied by a variable (in 7x - 5, coefficient is 7).
Solve: 5x = 35
x = 7
Solve: 3x - 4 = 11
x = 5
Maria earns $6 for each lawn she mows. Last week she earned $30. Let n be number of lawns. Write and solve an equation for n.
6n = 30 → n = 5 lawns.
Explain the difference between an expression and an equation. Provide one short example of each.
Expression: math phrase without "=" (e.g., 3x + 2). Equation: statement with "=" (e.g., 3x + 2 = 11).
Solve: x/4 = -3
x = -12
Solve: (1/2)x + 7 = 13
x = 12
A notebook costs $p each. You buy 3 notebooks and a pen for $2, paying $20 total. Write and solve an equation for p.
p + 2 = 20 → p = 6 dollars.
What is the Distributive Property? Write it as an algebraic rule (use variables).
Distributive Property: p(x + q) = px + pq.
Solve: -7 + x = 12
x = 19
Solve: -2x + 9 = 1
x = 4
The perimeter of a triangle is 48. The sides measure 15 , (2x + 3), and 15. Find x. (Write equation and solve.)
15 + (2x + 3) + 15 = 48 → x = 7
Define "rational number" and give two examples, one fraction and one decimal
Rational number: number that can be written as a ratio of integers (examples: 3/4, 0.25).
Solve: -3x = 9.
x = -3
Solve: 4(x - 3) = 20
x = 8
A store charges $4 shipping plus $2.50 per item. If a customer paid $19 for shipping and items, how many items did they buy? Write and solve an equation; show checks and reasoning.
4 + 2.5n = 19 → n = 6 items.